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A112111 G.f. A(x) satisfies A(A(A(A(A(x))))) = B(x) (5th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,4,5}, with B(0) = 0.

%I A112111 #6 Mar 13 2015 19:22:26
%S A112111 1,1,-3,17,-115,841,-6288,46174,-320366,1997348,-10216611,32418767,
%T A112111 68603755,-1909624513,15239954041,-103620859984,1499179409198,
%U A112111 -25808959095992,258001631302410,-239530586418995,-25424691109062239,84868851253494310
%N A112111 G.f. A(x) satisfies A(A(A(A(A(x))))) = B(x) (5th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,4,5}, with B(0) = 0.
%e A112111 A(x) = x + x^2 - 3*x^3 + 17*x^4 - 115*x^5 + 841*x^6 -6288*x^7 +...
%e A112111 where A(A(A(A(A(x))))) =
%e A112111 x + 5*x^2 + 5*x^3 + 5*x^4 + 5*x^5 + 5*x^6 + 4*x^7 + 3*x^8 +...
%e A112111 is the g.f. of A112110.
%o A112111 (PARI) {a(n,m=5)=local(F=x+x^2+x*O(x^n),G);if(n<1,0, for(k=3,n, G=F+x*O(x^k);for(i=1,m-1,G=subst(F,x,G)); F=F-((polcoeff(G,k)-1)\m)*x^k); return(polcoeff(F,n,x)))}
%Y A112111 Cf. A112110, A112104-A112109, A112112-A112127.
%K A112111 sign
%O A112111 1,3
%A A112111 _Paul D. Hanna_, Aug 27 2005